If Edward III had died by 1366, as in this scenario, his eldest son the 'Black Prince' does not become governor of Aquitaine for his father in the mid-1360s and so is not governing in Bordeaux when the refugee King Peter of Castile arrives to seek aid against his half-brother and deposer, the pro-French Henry of Trastamara. The choice of whether or not to invade Castile and get Peter's throne back for him was the BP's in OTL, though confirmed by his father the King, and the BP commanded the expeditionary force - and his long wait in Castile after his victory at Najera for Peter to pay his (huge) debts to the BP's army for their help probably led to his contracting the illness that killed him in 1376. So if Edward the BP is not in Castile in 1367, he probably does not fall ill as he was perfectly healthy until then - though he could easily pick up a debilitating condition on any campaign, especially in a hot climate or if there was an epidemic in camp (frequent with poor understanding of food preservation and hygiene or drinking from polluted rivers). The way that Edward fell into a deteriorating condition after summer 1367, was travelling by litter to his sack of rebel Limoges in 1370, then had to go home to England as an invalid, and was living quietly on his Home Counties estates taking no part in politics despite his father's mental decline in 1371-6 suggests an underlying physical weakness that fell easy prey to a medical problem - and his nephew Henry IV (his brother John of Gaunt's eldest son) had a similar physical collapse at a similar age (38-9 as opposed to Edward's 37) and died at 45/6 (Edward died at 46).
But assuming that Edward does not fall victim to some medical condition in different circumstances and probably does not go out to Spain at all but leaves it to his choice of governor in Aquitaine (probably Gaunt) to act, this would fling up some interesting possibilities. The Spanish campaign would probably still occur, as Castile was a crucial strategic ally across the Pyrenees from Aquitaine and if it was pro-French under Henry of Trastamara it could aid a French attack on Bordeaux by the anti-English new king as of 1364,
Charles V . It had also supplied naval aid to France in the Channel in the 1340s and tried to cut off the new English garrison at Calais - hence the then famous English naval battle against Castile off Winchelsea (known as 'The Battle of the Spaniards on the Sea' at the time, see Froissart) in August 1350. (Edward III commanded his navy in person and nearly drowned, another major 'What If', as his vessel was rammed by a bigger Castilian one and he had to lead his men aboard that and take it to avoid going down with his sinking ship.) So Edward the BP, as 'Edward IV', is bound to send English aid to drive Henry out of Castile and restore Peter; John of Gaunt probably leads it, and as in OTL would marry Peter's heiress Constance if he was then widowed.
But if John was in Bordeaux in 1368, the chances are against his first wife Blanche of Lancaster dying of the plague as in England in OTL. If he isn't free to marry Constance, he has no claims on the Castilian throne as the legitimist heiress' husband when Henry of Trastamara kills Peter in 1369; so probably Constance is married off to his younger brother Edmund of York, who in OTL married her next sister. It is Edmund not Gaunt who is therefore the English candidate to take over Castile from Henry's son in the mid- 1380s in a futile invasion - probably with no more success as he was a feeble general and no more than modestly competent in OTL. And if Gaunt is still married to a surviving Blanche in the 1370s, he probably does not have his children's governess Katherine Swynford as his mistress - so there are no Beaufort bastards to play a major role in C15th politics. If there is no line of Beauforts to claim the throne after the Lancastrian line, this deprives the latter of one major group of allies and the Yorkist line of one major block to their succession and one major challenge after Henry VI and his son are killed in 1471. At a long shot, there is no Tudor claim at all and no Henry VII to overthrow Richard III - though as Gaunt was a strong-willed, impulsive, and belligerent character who was notorious for self-willed actions he could still have had a mistress and provided a line of bastards to get involved in mid-late C15th politics. Alternatively, Gaunt could have had a younger son by Blanche and this person and his heirs would be next in line after Henry IV from 1399 - so when Henry VI has his collapse in 1453 the head of this branch,not Richard of York, is legal first in line to be regent. So we get a putative 'John, Duke of Somerset' (son of Henry IV' s putative younger brother and probably born c. 1400) as regent in 1453 and a far different , or no, power-struggle?
Gaunt being in command in Aquitaine through the 1370s (and even later?) means he is not available to be a divisive and resented figure in English politics, and as Edward III is not still king there is no weakening, faction-ridden government in 1370-6 headed by a mentally declining king open to abuse by greedy courtiers aligned to his unpopular mistress, Alice Perrers- and seen as aided by the main royal family centre of power and influence, Gaunt. Nor is there a regency for a 10-year-old Richard II, the BP's son, after 1377 with allegations of incompetence, poor leadership and muddle in the war with France, and extortionate and badly used taxes (again centred on Gaunt). In OTL there was a multiple socio-economic and political crisis as a result, exploding in the Peasants Revolt of 1381 and the rebels' rampage in London (and execution of ministers and sack of Gaunt's Savoy Palace). The govt was so poorly informed of provincial discontent by its local agents in the gentry elite that it was caught by surprise and had no time to raise loyal troops or any coherent reaction when the rebels marched on London - partly due to the eclipse of the close personal leadership of and relations with the local elites by Edward III and the BP as war-leaders from 1330 to c. 1370. If 'Edward IV' is still alive and a strong King, he is still in touch with the local elite, leading them in war, and respected as a national hero - at least the govt is warned of any provincial revolt in time to try to raise an army or shut the gates of London.
The lack of men and money available for the war as it resumed after 1369 could still lead to smaller armies and naval forces, failed marches across France by English armies unable (due to poor standards of 'new-fangled' cannons being unable to break down the walls of towns) to take places, and expensive campaigns achieving little. This would be a shock after the long run of triumphs in 1340-60 and lead to grumbling as in OTL, but fewer actual defeats are likely - eg the major naval disaster at la Rochelle in 1372 - as 'Edward IV' was a better judge of men, better general, and better selector of officers than the OTL weak English leadership of the 1370s. His determination to push on for victory and aggressive attitude to France could easily lead to excessive demands of men and money on a weak economic 'base', for little results, as in OTL - and some sort of popular uprising if hardly as early as 1381. Our putative 'Edward IV' was popular in the mid-1370s in real life even as an invalid living away from the (corrupt) court, and in the Parliamentary attack on Edward III's ministers and courtiers in the 'Good Parliament'in OTL 1376 he was believed to be backing reform and some of his old regional allies were involved in the demands. (He died during the Parliament so his actual attitude to it and to Gaunt's corrupt allies is unclear.)
Strong adult kings did sometimes face 'tax revolts' especially in wartime, as Henry VII did in 1497, though regencies (as 1381) and weak kings prone to faction (as 1450) were more vulnerable. An exhausting and unwinnable series of 'razzia' marches by English troops across France taking no major town , with the
French evading battle but 'Edward IV' still demanding ever more cash and troops, could still have led to an outbreak as per 1497 - and probably a similar outcome, ie a rebel camp on Blackheath SE of London, the gates of London and L Bridge shut and guarded, and eventually the rebels failing to go home as the King demands and him turning his troops on them with mass-killings. (Or , given Edward's high reputation, a negotiated settlement from a stronger Royal position than in OTL 1381?) But if Edward is alive into the late 1380s or 1390s, his son and heir Richard (born Jan 1367) is not King and at the centre of court flattery and factional intrigue from the age of ten but has a more normal childhood. He might still be insecure and (as not interested in warfare or military pursuits) at odds with his elite contemporaries and turn to resented 'outsider' favourites, as Edward II did - but he would not be King until his adulthood and would not be fearing that his uncle Gaunt was after his crown and trying to murder him. Richard would succeed as an adult, and his failings and reliance on disliked favourites and/or his demands for submission by all to his will would take longer to manifest. There would be no 1387-8 elite revolt against him, and so no coercion of him and execution of his friends leading to his counter-coup and executions and 'tyranny' in 1397. His preferance for abandoning an expensive war and signing peace with France might well still cause anger among his father's anti-French generals and their heirs , led by his uncle Thomas of Gloucester, so a 'showdown' like that of OTL 1399 is still possible. But this would take a different course if Richard was new to the throne c.1390-5 and had had a more normal upbringing.
